Research on optimal policy of single-period inventory management with two suppliers

We study a single-period inventory control problem with two independent suppliers. With the first supplier, the buyer incurs a high variable cost but negligible fixed cost; with the second supplier, the buyer incurs a lower variable cost but a positive fixed cost. At the same time, the ordering quantity is limited. We develop the optimal inventory control policy when the holding and shortage cost function is convex. We also conduct some numerical experiments to explore the effects of the fixed setup cost K and the ordering capacity Q on the optimal control policy.